The perturbation of transmission eigenvalues for inhomogeneous media in the presence of small penetrable inclusions

Fioralba Cakoni, Shari Moskow, Scott Rome

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

This paper concerns the transmission eigenvalue problem for an inhomogeneous media of compact support containing small penetrable homogeneous inclusions. Assuming that the inhomogeneous background media is known and smooth, we investigate how these small volume inclusions affect the real transmission eigenvalues. Note that for practical applications the real transmission eigenvalues are important since they can be measured from the scattering data. In particular, in addition to proving the convergence rate for the eigenvalues corresponding to the perturbed media as inclusions' volume goes to zero, we also provide the explicit first correction term in the asymptotic expansion for simple eigenvalues. The correction terms involves the eigenvalues and eigenvectors of the unperturbed known background as well as information about the location, size and refractive index of small inhomogeneities. Thus, our asymptotic formula has the potential to be used to recover information about small inclusions from a knowledge of real transmission eigenvalues.

Original languageEnglish (US)
Pages (from-to)725-748
Number of pages24
JournalInverse Problems and Imaging
Volume9
Issue number3
DOIs
StatePublished - Aug 1 2015

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

Keywords

  • Homogenization
  • Interior transmission problem
  • Inverse scattering problem
  • Periodic inhomogeneous medium
  • Transmission eigenvalues

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